As I have already asked once: what do you think the sin squared function represents? It's a simple question and you should be able to give a simple answer without another wall of text.Ian J Miller said:The joint probability is given sin squared
I am unable to recognize this as a reference to anything in Bell's "Bertlmann's socks" paper.Ian J Miller said:from Bell (pp 9 - 10 of the reference above) the initial position is the plus and minus detectors at right angles to each other.
Probability according to which theoretical model?Ian J Miller said:For an entangled pair, where one photon gives a click on the first detector, the sin squared function surely represents the probability that the partner photon will give a click on its detector
The reason you are having difficulty getting helpful responses is that nobody but you can understand how you are even getting to this belief in the first place. That's why I think it would be much better if, instead of trying to inundate us with your personal derivations, you would point us to explicit quotations and equations from whatever reference you are using that you think justify this belief of yours.Ian J Miller said:It is questioning how a term that should have a single value in the derivation of a relationship appears to have multiple values when these are used to argue that said mathematical relationship is violated.
PeterDonis said:Probability according to which theoretical model?
In the spirit of taking my own advice, I am going to give the answer to this question by quoting from Bell's Bertlmann's socks paper. I am using the PDF version that can be found on CERN's website [1].PeterDonis said:explicit quotations and equations
The quantum mechanical model does, yes.Ian J Miller said:The model involves the sin squared relationship.
No, as has already been pointed out, the QM model is not equivalent to Malus' law. That law is a classical approximation. You should not expect classical approximations to work for these experiments.Ian J Miller said:It is equivalent in this circumstance to the Malus law, which applies to a polarized wave.
Yes, because there he is calculating the quantum mechanical predictions for the correlations. Nothing he says that involves the sin squared function has anything whatever to do with deriving any inequalities. He is just showing that the QM prediction violates them.Ian J Miller said:The sin squared 22.5 and 45 degrees was used by Bell in the second equation of p 10.
What derivation? Where is this in the paper you referenced?Ian J Miller said:C- is a function, b ut in the derivation it occurs several times as a single term
Whether you want to post any further is of course up to you. But it seems to me that the reason for the difficulties in this thread is that you have insisted on using your own idiosyncratic derivation and notation that nobody else can understand, despite the fact that you referenced an actual paper. You could have given explicit equation numbers and quotations from text in that paper. But you didn't. The only time you have even talked about such things is when I forced you to by referencing them myself. And even then you only did it for a little bit, and then reverted to your former failed strategy, so that I have had to pose a follow-up question to you above that I shouldn't have had to pose at all.Ian J Miller said:I think it might be better if we terminate this discussion now because we are not discussing the same thing.
No, that's not Noether's theorem, that's just rotational invariance. Noether's theorem says that, because the laws of physics are rotationally invariant, angular momentum is conserved.Ian J Miller said:according to Noether's theorem, that is merely one result repeated.
The terms used in the inequalities are perfectly well defined: they are the actual observed correlations between the two measurements, for different settings of the measurement angles. If this wasn't well defined, how could the experimenters even collect and analyze the data?Ian J Miller said:Experimental tests are not relevant if the terms used are not clearly defined.
Why should I, or anyone actually doing these experiments, care about your derivation?Ian J Miller said:The derivation of the inequality I gave requires the terms to take one value under one set of circumstances.
The Bertlmann socks does not use the sin squared because there are no waves involved.PeterDonis said:The quantum mechanical model does, yes.
But the "Bertlmann's socks" model that is used to calculate the Bell and CHSH inequalities does not.
If you have not grasped this simple fact, you have not read the paper you referenced very carefully.No, as has already been pointed out, the QM model is not equivalent to Malus' law. That law is a classical approximation. You should not expect classical approximations to work for these experiments.Yes, because there he is calculating the quantum mechanical predictions for the correlations. Nothing he says that involves the sin squared function has anything whatever to do with deriving any inequalities. He is just showing that the QM prediction violates them.
Again, if you have not grasped this simple fact, you have not read the paper very carefully.What derivation? Where is this in the paper you referenced?Whether you want to post any further is of course up to you. But it seems to me that the reason for the difficulties in this thread is that you have insisted on using your own idiosyncratic derivation and notation that nobody else can understand, despite the fact that you referenced an actual paper. You could have given explicit equation numbers and quotations from text in that paper. But you didn't. The only time you have even talked about such things is when I forced you to by referencing them myself. And even then you only did it for a little bit, and then reverted to your former failed strategy, so that I have had to pose a follow-up question to you above that I shouldn't have had to pose at all.
Let me ask you this, then. If you did an experiment on one end of the bench and translated it to the other end, can you call that a new set of results, or are you reproducing the first result?PeterDonis said:No, that's not Noether's theorem, that's just rotational invariance. Noether's theorem says that, because the laws of physics are rotationally invariant, angular momentum is conserved.
Even with this correction, however, your claim here is wrong. Rotational invariance does not say that if run 2 of some experiment looks just like run 1 rotated by some angle, then they are really the same run. But that is what you are arguing here.
When you say, what is that thing? what do you think the above discussion is about? As an aside, I am not saying they are wrong; I am asking you why you and others think they are right.PeterDonis said:Why should I, or anyone actually doing these experiments, care about your derivation?
The people who actually do these experiments don't have any trouble understanding what the terms in the inequalities mean, or how the inequalities were derived, or how to calculate the numerical values from their data. If you are correct, they must all be doing something obviously wrong. What is that thing?
Wrong. It doesn't use the sin squared because it is not a quantum model, it is a local hidden variable model.Ian J Miller said:The Bertlmann socks does not use the sin squared because there are no waves involved.
For this particular case, perhaps. That still doesn't mean you can expect to apply classical reasoning to a quantum model.Ian J Miller said:You say the QM model is not equivalent to the Malus law, but it counts joint probabilities with the same function.
Then I fail to see why you keep talking about it, since your point, to the extent you have a coherent point, appears to be that there is something about the way the inequalities are derived that makes them somehow not apply the way they are claimed to apply to the experiments that are supposed to test them.Ian J Miller said:I never said the sin squared was involved in deriving the inequality
Do you mean, move to the other end of the bench and then do another experiment that has (to within experimental error) the same initial conditions and measurements?Ian J Miller said:If you did an experiment on one end of the bench and translated it to the other end
Both. I am generating a second set of results, which, given the identical initial conditions and measurements and the fact that the laws of physics are translation invariant, I expect to be identical, to within experimental error, with the first set of results.Ian J Miller said:can you call that a new set of results, or are you reproducing the first result?
I have no idea. That's why I keep asking you to actually quote equations and text from the paper you referenced in order to make whatever point you are trying to make. I understand the paper you referenced, so if you are quoting equations and text from that, I will at least be able to start from a point that I understand, in order to try to grasp whatever point you are trying to make. When you insist on trying to make your point using your own idiosyncratic notation and your own made up derivations, on the other hand, I have no point to start from at all, since I can't make sense of either your notation or your derivations.Ian J Miller said:When you say, what is that thing? what do you think the above discussion is about?
Um, because I and others (including the theorists and experimenters themselves) understand the derivations and equations and arguments they are using and agree that they are correct?Ian J Miller said:I am asking you why you and others think they are right.
I strongly doubt that. I strongly doubt that it is beyond your ability to quote some actual equations and text from the paper you reference that will illustrate whatever point you think you are trying to make.Ian J Miller said:I have explained my problem to the best of my ability.
I have already explained why that is, multiple times now. See above.Ian J Miller said:So far, nobody seems to understand the question I am putting
To sharpen the question I ask at the end of this quote, let me run with the implied analogy you made here. In the case of the experiments described in Bell's Bertlmann's socks paper, we have two sets of runs where the difference in angles is the same, 45 degrees: we have runs where one measurement is done at 0 degrees and one is done at 45 degrees, and we have runs where one measurement is done at 45 degrees and one is done at 90 degrees. Rotational invariance says that, to within experimental error, the correlations observed in both sets of runs should be the same.PeterDonis said:Both. I am generating a second set of results, which, given the identical initial conditions and measurements and the fact that the laws of physics are translation invariant, I expect to be identical, to within experimental error, with the first set of results.
What is your point with all this?
PeterDonis said:Wrong. It doesn't use the sin squared because it is not a quantum model, it is a local hidden variable model.
For this particular case, perhaps. That still doesn't mean you can expect to apply classical reasoning to a quantum model.Then I fail to see why you keep talking about it, since your point, to the extent you have a coherent point, appears to be that there is something about the way the inequalities are derived that makes them somehow not apply the way they are claimed to apply to the experiments that are supposed to test them.Do you mean, move to the other end of the bench and then do another experiment that has (to within experimental error) the same initial conditions and measurements?
In what follows, I'll assume that the answer is yes.Both. I am generating a second set of results, which, given the identical initial conditions and measurements and the fact that the laws of physics are translation invariant, I expect to be identical, to within experimental error, with the first set of results.
What is your point with all this?I have no idea. That's why I keep asking you to actually quote equations and text from the paper you referenced in order to make whatever point you are trying to make. I understand the paper you referenced, so if you are quoting equations and text from that, I will at least be able to start from a point that I understand, in order to try to grasp whatever point you are trying to make. When you insist on trying to make your point using your own idiosyncratic notation and your own made up derivations, on the other hand, I have no point to start from at all, since I can't make sense of either your notation or your derivations.Um, because I and others (including the theorists and experimenters themselves) understand the derivations and equations and arguments they are using and agree that they are correct?
Everything is laid out right there in Bell's papers. What's wrong with his arguments? In my opinion, and apparently in the opinion of the theorists and experimenters in this field who have spent several decades now doing more and more accurate experiments and confirming everything Bell said, nothing. Isn't that a good enough reason to think they are right?I strongly doubt that. I strongly doubt that it is beyond your ability to quote some actual equations and text from the paper you reference that will illustrate whatever point you think you are trying to make.
More precisely, I strongly doubt that would be beyond your ability, if you had an actual coherent point to make. So the fact that you have not done this obvious thing just indicates to me that you do not.I have already explained why that is, multiple times now. See above.
Now I am more confused. Bertlmann's socks were washed at three different temperatures. The degrees are degrees C, or K, not angles.PeterDonis said:To sharpen the question I ask at the end of this quote, let me run with the implied analogy you made here. In the case of the experiments described in Bell's Bertlmann's socks paper, we have two sets of runs where the difference in angles is the same, 45 degrees: we have runs where one measurement is done at 0 degrees and one is done at 45 degrees, and we have runs where one measurement is done at 45 degrees and one is done at 90 degrees. Rotational invariance says that, to within experimental error, the correlations observed in both sets of runs should be the same.
But rotational invariance does not tell us what those correlations should be, numerically. For that, we need a theoretical model. And both theoretical models that Bell uses in his paper, the QM one and the Bertlmann's socks one, satisfy rotational invariance: both of them predict that the correlations in both sets of runs described above should be the same. But they predict different numerical values for those correlations: the QM model predicts a correlation of ##\sin^2 22.5 / 2##, or ##.0732##, for both sets of runs, while the Bertlmann's socks model predicts a correlation of ##22.5 / 180## (since we're using degrees, the denominator is ##180## instead of ##\pi##), or ##.125##, for both sets of runs. Rotational invariance gives us no help at all in deciding between these theoretical models. So what's the point of bringing it up?
Bell starts out describing it that way, but he then points out that exactly the same logic that the socks model applies to socks, can be used to build a model of spin measurements at different angles, of the kind that are made in EPR experiments. So the properties of the socks model can also be used to derive predictions about correlations in such spin measurements. And, as he points out, those predictions are different from the QM predictions; the "socks model" predictions obey inequalities that the QM predictions violate.Ian J Miller said:Bertlmann's socks were washed at three different temperatures. The degrees are degrees C, or K, not angles.
No, that is not what Ehrenfest's theorem says. The equation he derived for expectation values only follows the same relationships as classical physics for certain expectation values under certain conditions. The claim you are making here is much stronger than that.Ian J Miller said:The connection between classical and quantum physics is that if sufficient data are obtained that you can get expectation or average values, then these expectation values follow the relationships of classical physics. (Ehrenfest
No, your claim that it is "repeating the same experiment" is simply an assertion (and an unsupported and unfounded one). The experimental fact is that the detectors were rotated, and the experiment after the rotation was a separate experiment from the original one before the rotation. Recording the data from the two separate experiments as separate data is just being honest about what you actually did when the experiments were done.Ian J Miller said:if you rotate both detectors in what you assign as the A+B- experiment, you are repeating the A+B- experiment, and indeed you get the same answer. To call it B+C- is simply an assertion.
That is correct, yes; the observed correlations that are then compared with theoretical predictions are obtained this way (at least that's my understanding). And those observations are made (at least in experiments that are intended to test inequalities like CHSH) with 3 different pairs of angles, which Bell takes to be 0 and 45 degrees, 45 and 90 degrees, and 0 and 90 degrees. The fact that two of these three pairs are predicted (by both theoretical models in view) to give the same correlations (but with different numerical values for the correlations in the two different models), because of rotational invariance, does not change the fact that there are three distinct experimental runs, each of which gives its own measured correlation that then has to be compared with theoretical predictions. Rotational invariance, as I said in post #52 just now, is simply one of the theoretical predictions (and of course is found to hold).Ian J Miller said:I was under the impression that the observed counts at the detectors, i.e. the count at detector 1, and the count at detector 2 arriving within x ns of a click at detector 1, were used to evaluate joint probabilities. These are simple measurements, with no theoretical model required.
Of course I realize the sock model obeys the inequality, and the QM model does not, BUT the QM model only disobeys the inequality because the rotation of the polarizers in a set configuration when the source is rotationally invariant is allowed to introduce two new variables, when the only frame of reference, the angle between the two detectors, has also been rotated. My point is that if the source is polarized, i.e. it defines a fixed external frame of reference, the inequality is complied with. How can that happen, other than in one of the two cases something has gone wrong?PeterDonis said:Bell starts out describing it that way, but he then points out that exactly the same logic that the socks model applies to socks, can be used to build a model of spin measurements at different angles, of the kind that are made in EPR experiments. So the properties of the socks model can also be used to derive predictions about correlations in such spin measurements. And, as he points out, those predictions are different from the QM predictions; the "socks model" predictions obey inequalities that the QM predictions violate.
That is literally the primary point of the paper you referenced. I am flabbergasted that you don't realize that since it is absolutely essential to understanding what Bell was talking about.
If simply rotating the detectors against a rotationally invariant background generates the two new variables then you have provided your answer to the original question. Thank you.PeterDonis said:No, your claim that it is "repeating the same experiment" is simply an assertion (and an unsupported and unfounded one). The experimental fact is that the detectors were rotated, and the experiment after the rotation was a separate experiment from the original one before the rotation. Recording the data from the two separate experiments as separate data is just being honest about what you actually did when the experiments were done.
Using rotational invariance to argue that the correlations from both experiments will be the same is a theoretical prediction, which then has to be compared with the actual experimental facts to see if it holds. You can't assert that they are "the same experiment", because that isn't what rotational invariance says anyway. Rotational invariance does not say that the two experiments, one before rotating the detectors and one after, are "the same experiment". It just says that those two separate experiments will give the same correlations.
What is your basis for this claim?Ian J Miller said:if the source is polarized, i.e. it defines a fixed external frame of reference, the inequality is complied with.
Um, what? Seriously? That was the issue? And now, from that one simple statement, you're convinced it's no longer an issue?Ian J Miller said:If simply rotating the detectors against a rotationally invariant background generates the two new variables then you have provided your answer to the original question. Thank you.
I thought I put that up earlier, however, if this is a repeat, forgive me. There is no experiment as far as I know because nobody has tried it, but:PeterDonis said:What is your basis for this claim?
I was hoping to end the discussion.PeterDonis said:Um, what? Seriously? That was the issue? And now, from that one simple statement, you're convinced it's no longer an issue?
There is no such thing. If you restrict the polarization to one plane, there is no way to get an entangled state.Ian J Miller said:Assume a source that provides entangled photons, all of which are polarized in one plane.
Does that mean that the issue you were concerned about is no longer an issue?Ian J Miller said:I was hoping to end the discussion.